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Results tagged with block-matrices
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user 9025
2
votes
Non-singular matrix with restricted entries
[EXPANDED]
PART 1 (also done by Peter)
If $x,y$ are coprime and have opposite sign, there is a singular symmetric matrix with 1 on the diagonal and
only $x$ and $y$ off the diagonal.
Say $x<0,y>0$. Si …
- 37.7k
3
votes
When does $\det \begin{pmatrix} A & X \\ X^T & A \end{pmatrix} = (\det A)^2 + (\det X)^2$?
$$B=\left[\matrix{1&1&1&1\\1&1&-1&-1\\-1&-1&-1&1\\-1&1&-1&1}\right]$$
and probably many other solutions. I'm also voting to close because you didn't pose a research-level problem. If you have an int …
- 37.7k